The purpose of this research project is to develop new and efficient computer algorithms which can perform exact nonparametric inference for a wide range of important biostatistical problems. We will be concerned with exact significance testing and exact confidence interval estimation in situations where two or more populations are being compared by nonparametric methods. The data forming the basis of the comparisons may be ordered or unordered. Ordered data may be categorical continuous. Finally, the continuous data may be censored or complete. The techniques developed here are especially relevant when the number of observations in one or more of the populations are small, thereby casting doubt on the validity of the various asymptotic tests conventionally used for these problems. The marvelous improvements in computer technology over the past decade have had a major impact on both the direction of methodologic research in biostatistics and on the manner in which statisticians analyze data. The major significance of the present research plan is that it exploits the opportunities provided by the easy availability of computer hardware and develops efficient numerical algorithms for statistical computing. These algorithms will enable practicing statisticians to use exact analysis whenever the data are too sparse to rely on asymptotic theory, and will give theoretical statisticians bench marks against which to compare their asymptotic results. The following problem areas of direct relevance to the analysis of cancer clinical trials and case-control studies, will be investigated: (l) the exact Wilcoxon test and the exact sign test for stratified, ordered categorical data, and continuous data; (2) estimation of exact confidence intervals for odds ratios associated with several 2xc contingency tables; (3) exact nonparametric group sequential procedures for early stopping of clinical trials; (4) exact tests for comparing r populations in one way and two way layouts with ordered categorical data and complete or censored survival data; (5) exact inference in unordered rxc contingency tables. Algorithms for the problem areas will be developed on the basis of network optimization supplemented by hybrid and Monte Carlo techniques.